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Chapter 17
The First Law of Thermodynamics
Thermodynamic Concepts
• Thermodynamic system:
able to exchange heat with its surroundings
• State variables: p, V, T, ...
describe the thermodynamic system
• Thermodynamic process:
changes the state ( p, V, T, ...) of the system
Thermodynamic Process
Heat Q:
can leave or enter system
Work W:
• system can do work on its surroundings
• surroundings can do work on the system
thermodynamic
system:
can exchange
heat with its
surroundings
state of system:
(p, V, T, ...)
thermodynamic
process:
changes state
of the system
thermodynamic
process:
changes state
of the system
We’ll focus on
the roles of:
• Heat Q
• Work W
Heat Q:
can leave or
enter system
Q > 0:
heat added
to system
Q < 0:
heat removed
from system
Sign Conventions for Q
Q > 0: heat added to system
Q < 0: heat removed from system
• Consistent with sign of DT from earlier:
Q = mc DT or Q = nC DT
Work W:
W > 0:
system does
work on its
surroundings
W < 0:
surroundings
does work on
the system
Sign Conventions for W
W > 0: system does work on surroundings
W < 0: surroundings does work on system
• (the ‘opposite perspective’ as in mechanics)
(a) Q > 0, W = 0
(b) Q < 0, W = 0
(c) Q = 0, W > 0
(d) Q = 0, W < 0
(e) Q > 0, W > 0
(f) Q < 0, W < 0
Work done when volume changes
dW  Fdx  ( pA)dx
 p( Adx)
 pdV
Work done when volume changes
dW  pdV
2
W   pdV
1
Work done when volume changes
dW  pdV
2
W   pdV
1
Work W is path-dependent
dW  pdV
2
W   pdV
1
• W = area under graph of the function p(V)
• W depends on initial and final states (1, 2)
• W depends on path taken (intermediate states)
Q (= heat transferred)
is also path-dependent
Thermodynamic Concepts
• Thermodynamic system:
described by state variables (p, V, T, ..)
• Thermodynamic process:
changes the state ( p, V, T, ...) of the system
• Heat Q, Work W:
‘path-dependent’: values depend on process
Heat Q and Work W
• Q and W are not properties of the system
(Q enters or leaves the system)
(W is done on or by the system)
• We can measure the difference: Q – W
• Q – W is related to a property of the system
Q–W
• We choose a thermodynamic system
• We take the system between a fixed initial
final state for many different processes
• For each process, we measure Q – W
• Experiment surprises us!
Q–W
• For this setup, we always find:
• Q – W has same value for all processes
• Q – W depends only on initial, final state
• Q – W is path-independent
(these are three equivalent statements)
Q–W
Since Q – W depends only on state variables:
Q – W = a change in a property of the system
We define U = ‘internal energy’ of system:
Q – W = DU
First Law of Thermodynamics
Q – W = DU
or
Q = W + DU
• Generalizes conservation of energy from just
mechanical energy to include heat energy
First Law of Thermodynamics
Q – W = DU
or
Q = W + DU
• The heat energy Q added to a system goes
into work W and change in internal energy U
First Law of Thermodynamics
Q – W = DU
or
Q = W + DU
• (Notation: U is not simply ‘potential energy’)
Laws of Thermodynamics
Zeroth Law:
‘every thermodynamic system has a property
called temperature T’
First Law:
DU = Q – W
‘every thermodynamic system has a property
called internal energy U’
DU = Q – W
Recall:
• Q can be > 0, < 0, = 0
• W can be > 0, < 0, = 0
Thus:
• DU can be > 0, < 0, = 0
Free Expansion
• Break partition
• Let gas expand
freely into vacuum
Free Expansion
• gas is in
equilibrium at
initial and final
states
• gas is not in
equilibrium
between initial and
final states
Free Expansion
• Set-up for process:
Q = 0 (insulation)
W = 0 (no pushing)
• First Law says:
DU = Q – W = 0
Free Expansion
• For the gas:
Dp , DV are nonzero
• Experiment shows:
• low density (‘ideal’)
gases have DT = 0
between initial and
final states
Free Expansion
• For the gas:
Dp , DV are nonzero
• Experiment: DT = 0
• First Law: DU = 0
• Conclude: For an
ideal gas, U only
depends on T
Laws of Thermodynamics
Zeroth Law:
‘every thermodynamic system has a property
called temperature T’
First Law:
DU = Q – W
‘every thermodynamic system has a property
called internal energy U’
First Law of Thermodynamics
Q – W = DU
or
Q = W + DU
• Generalizes conservation of energy:
• Heat energy Q added to a system goes into
both work W and change in internal energy U
Thermodynamic Processes
Process
Free Expansion:
Cyclic:
Definition
Q=0
W=0
closed loop
Consequence
DU = 0
DU = 0
Q=0+W
Thermodynamic Processes
Process
Definition
Consequence
Isobaric
p = constant
W = p DV
Isochoric
V = constant
W=0
Q = DU + 0
Thermodynamic Processes
Process
Definition
Consequence
Isothermal
T = constant
(must be slow)
DU = 0
Adiabatic
Q=0
(insulated or fast)
0 = DU + W
Molar Heat Capacity Revisited
Q = n C DT
• Q = energy needed to heat/cool n moles by DT
• CV = molar heat capacity at constant volume
• Cp = molar heat capacity at constant pressure
CV for Ideal Gases, Revisited
Molecular Theory:
(Ktot)av = (f/2) nRT
CV = (f/2)R
Monatomic: f = 3
Diatomic:
f = 3, 5, 7
New language:
U = (f/2) nRT
CV = (f/2)R
Monatomic: f = 3
Diatomic:
f = 3, 5, 7
Cp for Ideal Gases
• We expect:
Cp > CV
• Example:
gas does work expanding against atmosphere
• We can show:
Cp = CV + R
Derive this result
Cp for Ideal Gases
C p  CV  R
CV  R


CV
CV
Cp
• monatomic gas:
CV = (3/2)R
(5 / 2) R 5

  1.67
(3 / 2) R 3
• diatomic gas:
at low T, CV = (5/2)R
(7 / 2) R 7

  1.40
(5 / 2) R 5
Adiabatic Process (Q = 0)
• An adiabatic process for an ideal gas obeys:
TV  -1 = constant value
pV  = another constant
Derive these results
Adiabatic Process (Q = 0)
For an ideal gas undergoing an adiabatic process:
W  nCV (T1 - T2 )
CV

( p1V1 - p2V2 )
R
1

( p1V1 - p2V2 )
 -1
Derive these results
Derive some isobaric results
Do Problem 17-42